The path taken by a ray of light, from an event E1 to event E2, follows a zero arc length curve such that(adsbygoogle = window.adsbygoogle || []).push({});

E2

∫ds = 0 1.

E1

Where S is the interval along the null geodesic path between the two events

If we fix E1 and let E2 take any value E; then all the Es form a wave front emanating from E1.

In the case of Minkowski space-time: -

deltas2 = c^2deltat^2 – deltax^2-deltay^2-deltaz^2 2.

deltas^2 becomes zero when: -

c^2Ct^2 = deltax^2-deltay^2-deltaz^2 3. (see attachment)

for a given event E1(X1, Y1, Z1, T1) then all values of E (X, Y, Z, T) fulfilling this requirement form a light cone.

Now consider a “particle” P passing through E1, the particle will have zero interval separation with all events E. The state P may be influenced by the states of all E through electromagnetism. By absorbing energy from the past region of E or donating energy to the future Es.

Let us now imagine that associated with the donation and absorption of energy is a frequency which relates to the energy level according to Planck’s relationship: -

E = hn 3.

The particle P will interact to either absorb or donate energy, at frequency n if it comes in contact with a system that will also respond to the given frequency. Since event E1 is contiguous through zero arc length with all locations E then P is causally linked to all systems existing on the light cone E. This does not mean that P will necessarily interact with these systems but it does mean that P can potentially interact with them if the state of P and states of systems on E are mutually amenable to interaction.

The path of P passes through E1, when the state of P can potentially influence any system existing(all system) on the light cone formed by equation 1. P will pass through E1 and equation 1. will generate light cones from every point on the track of P. Lets us assume that there is a phase associated with the P as well as a frequency. P will interact with other systems if they amongst other things have states that will also respond to the same frequency and phase as P. As P passes along its world line its likelihood of interaction will vary with phase. Equation 1. will transmit the information about the state of P across successive light cones. This wave function will be generated indefinitely until P finds a suitable system with which it can interact. Following interaction, equation 1. will transmit the information regarding the new state of P. We note that equation 1 allows immediate an direct interaction between “spatially remote particles”

We can compare with Bohmian mechanics; our equation

E2

∫ds = 0 1.

E1

Effectively defines the pilot wave, this fills the whole of space-time (when secondary wave generation is taken into account) the actual interactions are between pairs (or more) of particles. The energy is transmitted directly between quantum systems and the photon does not have any independent identity. Being merely the energy that is transmitted directly between contiguous quantum systems!

We note also that although we referred to our particle existing at event E1 in reality relative to our coordinate systems, if equation 1. correctly defines the causal links between events then a particle cannot be said to be uniquely present at a given event. This because any event E is causally linked to all events lying on the light cone passing through E! A quantum event affecting a particle therefore must take on the form of a light cone where the likelihood of the particle interacting with another particle is higher the nearer the second particle is to the apex of the cone.

Personally I believe the zero arc length mediation is the most plausible explanation of electromagnetism. It seems to explain many of the bizarre and counter intuitive aspects of physics and without having to include arbitrary augmentation such as hidden dimensions, many worlds etc. It appears to explain single particle interference and is consistent with the violation of Bell’s inequality and is still founded soundly on general and special relativity, though with equation 1. taking on a special significance. It is difficult to believe that zero arc length mediation of electromagnetism is not the front runner in the search for reconciliation between relativity and quantum mechanics?

Maths is scrambled see attatchment

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# Does zero arc length mediation of EM cause the wavefunction

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